This invention relates generally to solving logistical operations problems in three dimensional (3D) land seismic surveys. More particularly, the invention is a method and system for optimizing seismic surveys by applying operations research methodologies to the land seismic surveying problem domain. Optimization problems in 3D land seismic surveying are formulated and solved using mathematical programming techniques. The invention introduces a number of optimization models and methods for improving logistical operations in 3D land seismic surveys. The present method and system models logistical problems by formulating the problem as a set of inequalities and then solving the set of inequalities using an optimization software program using mathematical programming techniques.
Seismic surveying is a key technology area in geophysical prospecting. Seismic surveying is primarily concerned with reflection seismology. A source on the surface of the earth generates a signal which propagates through the earth. The underground geological structures attenuate, reflect, and refract the signal. Receiver equipment on the earth's surface monitors the reflected wave. Using this and other information, seismologists construct a picture of the earth's subsurface.
Over the years, increasingly sophisticated survey designs and data processing techniques have been developed. More sophisticated designs have led to more complex logistical operations in conducting seismic surveys. For example, until the early 1980's, most land seismic surveys were two dimensional (2D) surveys conducted along a single line of source and receiver points. Today, most surveys are three dimensional (3D) where source and receivers points are scattered on a plane and the arrangement of the source and receiver points is defined by the requirements of the survey.
The requirements of seismic surveying can be subdivided into two categories: geophysical and logistical. A great deal of the formal research has focused on improving the geophysical aspect of seismic surveys. The geophysical aspect involves achieving the best possible signal to construct the best possible picture of the earth's subsurface. Many improvements have been made in seismic signal source generation and receiver detection technology. In seismic surveying, a signal is generated from a source point, follows along a ray path, and is reflected off an underground target level. The reflected path returns to a receiver point. The reflected signal provides information on the underground structure such as a subsurface layer. The point of reflection of the underground target between the source and receiver is called the common midpoint (CMP). In seismic surveying, several receivers are turned on to detect the signal sent out from a single source point. This permits the simultaneous sampling of several CMPS. If the process is repeated with several sources instead of one source, then the same CMPs get sampled several times. Sampling on the same point improves the signal-to-noise ratio (S/N) for the processing of the data and results in better signal strength, which gives a better picture of the earth's subsurface.
Much less emphasis has been placed on logistical operations and on techniques for improving those operations. The logistical aspect relates to the handling of the details of the seismic surveying operation along with any other factors besides geophysical ones that affect survey results. Among the many factors that influence the logistics of a survey are size of the survey, design of the survey, the amount of equipment available, and the number of crews available. These factors are controllable. Other factors that affect the survey results such as weather, terrain and underground geology are not controllable.
Operations on a land seismic survey involve the coordination of signal generation (shooting), placement of equipment to receive the reflected signal, and recording of the results. The logistics center of a survey is called base camp. Line crews place the equipment (channels) on the ground and use vehicles referred to as line trucks. The equipment consists of cables, receivers and boxes. Boxes collect data and perform analog to digital conversion and filtering of the data. The boxes are powered by batteries and solar panels. Source crews (sets of vibrators or dynamite shooting crews) progress through a preplanned sequence of source locations. An acquisition system, located in a recording platform, turns different receivers on and off so that the required set of receivers that monitors a single source (called a patch) is turned on for each source measurement. The acquisition system also records the results from each shot. Line crews move equipment in the direction of the progression of the survey. Typically, there is not enough equipment available to cover the entire survey area. Thus, equipment movement is required. Measurements from a single source point typically take less than one minute. Movement of receiving equipment from one patch to the next one in the shooting sequence can take several minutes. Therefore, extra equipment is used to cover several patches ahead of the current source location.
Given the high cost of performing seismic surveys, optimizing the operational as well as the geophysical aspects of the surveys is increasingly important. Because of the number of geophysical and logistical factors that influence survey results, including customer requirements and the complexity of optimization due to those factors, there is a need to develop computer models for survey optimization. The computer model needs to optimize survey operation, for example, by conducting a survey at the lowest possible cost or generating the highest possible profit, while maintaining the geophysical survey requirements.
One of the ways to formulate and solve optimization problems in 3D land seismic surveys is by using operational research mathematical programming techniques. Mathematical programming has been widely applied to solve operations problems in manufacturing, transportation and logistics, finance, and marketing where the parameters are quantifiable. Mathematical programming techniques can be used when a problem is formulated as: (i) a set of decision variables, (ii) a problem specification to be solved that is expressed as a function to be minimized or maximized (called objective function), and (iii) a set of constraints. Decision variables are quantities under the control of the decision maker. Examples of decision variables are factors such as size of the survey, the design of the survey, the amount of equipment available, and the number of crews available. It is these controllable factors that provide the decision maker with the opportunity to improve or even optimize survey design and operations. The constraints are the restrictions that bound the problem, for example, the maximum number of signals that can be generated in a day (called the number of shots). The problem specification is essentially a set of inequalities modeling the general logistical problem to be solved. Examples of problem specifications that can be modeled using sets of inequalities include: minimization of total costs in the design and operations of a land seismic survey; the optimal routing of one or more source crews through a sequence of source location points; the optimal placement of recording locations in a survey; and the optimal amount of an expendable resource to purchase prior to the survey so there is a sufficient amount of the resource available for the survey with a minimal amount remaining. These inequalities take into account the decision variables and constraints corresponding to the particular instance of the problem to be solved. Other quantities in the inequalities, called problem data or parameters, are not computed but are set to given values or a set of values. An example of problem data might be the surveying costs for every source and receiver point. After the problem is modeled as a set of inequalities, it is translated into a form suitable for solution by a solver using, for example, an algebraic modeling language. The solver then computes the values of the decision variables which optimize the objective function and satisfy the set of constraints. The values of the decision variables are computed such that the objective function is optimized and the set of constraints is satisfied. The result is an improved survey design and logistical operation.
Models become harder to solve when the decision variables are integer, the objective function and/or the constraints are nonlinear, and the problem data are stochastically defined. For integer programming problems, the computational complexity of the solution grows exponentially with the number of integer variables. No algorithm can solve all nonlinear programming problems to optimality. The best any algorithm can do in the general case is to guarantee local optimality (such as guarantee the best solution over a local region of possibilities). In certain special cases when the objective function has a special shape or structure, leading for example to the property of convexity, global optimality (the best solution over all possibilities) can also be guaranteed. To eliminate uncertainty in the data, assumptions may need to be made but may result in solutions that are far from optimal. Stochastic programming techniques use the structure of the mathematical model to furnish exact solutions or simulation (Monte Carlo sampling) to bound the optimal solution. Given all these complicating factors, an optimal solution, or a solution within a specified tolerance of the best possible solution, or just a feasible solution, that is, one that satisfies the problem constraints is sought.
Many types of commercial optimization software packages (also called solvers) exist to solve mathematical programming problems. Once the mathematical model has been formulated, it must be input to a solver. Spreadsheet packages incorporate solvers and can be used to solve small (generally less than 200 variables) 3D seismic surveying problems. For larger problems, algebraic modeling languages such as GAMS (Brooke et al. 1992) or AMPL (Fourer et al. 1993) may be required. Alternatively, a program can be written to directly call a commercially available solver library.
Problems amenable to mathematical programming techniques abound in land seismic operations. Vehicle routing problem formulations used in transportation may be adapted to the vehicles used in moving the equipment and in the shooting operations. Models used in logistics for facility locations may be used to determine the location and moves of the base camp and trucks carrying the recording system. Other problems include crew shuttling to and from remote locations, line crew scheduling, battery replacement strategies in the data recording boxes, and the balancing of workloads between line crews, line trucks, and source crews. Ultimately optimization modeling may be used to design seismic survey strategies that differ from those specified by geophysical criteria alone. For example, a seismic survey design may be developed by incorporating all costs (including cost of operations) that would ensure a certain fold coverage, offset distribution, and azimuthal distribution.